Panconnectivity and Pancyclicity of Hypercube-Like Interconnection Networks with Faulty Elements
In this paper, we deal with the graph G 0 ⊕G 1 obtained from merging two graphs G 0 and G 1 with n vertices each by n pairwise nonadjacent edges joining vertices in G 0 and vertices in G 1. The main problems studied are how fault-panconnectivity and fault-pancyclicity of G 0 and G 1 are translated into fault-panconnectivity and fault-pancyclicity of G 0 ⊕G 1, respectively. Applying our results to a subclass of hypercube-like interconnection networks called restricted HL-graphs, we show that in a restricted HL-graph G of degree m (≥3), each pair of vertices are joined by a path in G \F of every length from 2m–3 to |V(G \F)| − 1 for any set F of faulty elements (vertices and/or edges) with |F| ≤m–3, and there exists a cycle of every length from 4 to |V(G \F)| for any fault set F with |F| ≤m–2.
KeywordsInterconnection Network Hamiltonian Cycle Free Edge Longe Path Hamiltonian Path
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- 3.Bondy, J.A., Murty, U.S.R.: Graph Theory with Applications, 5th printing, American Elsevier Publishing Co., Inc., (1976)Google Scholar
- 8.Hsieh, S.-Y., Chang, N.-W.: Cycle embedding on the Möbius cube with both faulty nodes and faulty edges. In: Proc. of 11th International Conference on Parallel and Distributed Systems ICPADS 2005 (2005)Google Scholar
- 12.Park, J.-H.: Cycle embedding of faulty recursive circulants. Journal of KISS 31(2), 86–94 (2004) (in Korean)Google Scholar
- 13.Park, J.-H., Kim, H.-C., Lim, H.-S.: Fault-hamiltonicity of hypercube-like interconnection networks. In: Proc. of IEEE International Parallel and Distributed Processing Symposium IPDPS 2005, Denver (April 2005)Google Scholar
- 16.Vaidya, A.S., Rao, P.S.N., Shankar, S.R.: A class of hypercube-like networks. In: Proc. of the 5th IEEE Symposium on Parallel and Distributed Processing SPDP 1993, December 1993, pp. 800–803 (1993)Google Scholar